From [X, Py] = 0 follows that i can build a simultaneous autoket of X and Py (momentum on Y axis). Should i expect to observe a particle on X axis and a wave on Y axis? Does it make any sense?

I don't think it makes sense. There is no experimental procedure for "observing a particle" or "observing a wave". In experiment one can measure particle positions, momenta, spins, and other observables. Moreover, in QM these measurements are essentially probabilistic: If measurements are performed on an ensemble of identically prepared systems, one often obtains different results for different members in the ensemble.

If you want your question to have a definite answer you should formulate it within this experimental context.